Playwright: fix request utils for non Docker envs

[ellatrix]

What?

For non Docker installs theme activation fails: the path assumes the base URL to be simply the host while WP could be installed in a directory. It also assumes the theme won't be located in a subdirectory.
Extracting this out of #47907 to isolate test failures.

Why?

How?

Testing Instructions

Use MAMP: https://github.com/WordPress/gutenberg/blob/9a4b95e37da8b4c4b271f510895690a4ea1fa780/docs/contributors/code/getting-started-with-code-contribution.md#using-local-or-mamp

Testing Instructions for Keyboard

Screenshots or screencast

[github-actions]

Flaky tests detected in e6f0da3.
Some tests passed with failed attempts. The failures may not be related to this commit but are still reported for visibility. See the documentation for more information.

🔍 Workflow run URL: https://github.com/WordPress/gutenberg/actions/runs/4230101622
📝 Reported issues:

• [Flaky Test] should navigate block hierarchy using only the keyboard #47640 in specs/editor/various/block-hierarchy-navigation.test.js
• [Flaky Test] shouldn't conflict with server-side autosave #35176 in specs/editor/various/autosave.test.js

[kevin940726]

Nice, thanks! Any idea how we can test this?

[ellatrix]

@kevin940726 I'm testing it with MAMP: https://github.com/WordPress/gutenberg/blob/9a4b95e37da8b4c4b271f510895690a4ea1fa780/docs/contributors/code/getting-started-with-code-contribution.md#using-local-or-mamp

[kevin940726]

I'm gonna just trust you on that then 😆 .

[ntsekouras]

I just cherry-picked this PR to the wp/6.2 branch.